U.S. patent application number 17/047405 was filed with the patent office on 2021-04-22 for subdomain hybrid cellular automata method for solving car body thickness optimization.
This patent application is currently assigned to JIANGSU UNIVERSITY. The applicant listed for this patent is JIANGSU UNIVERSITY. Invention is credited to Libin DUAN, Haobin JIANG, Xin LUO.
Application Number | 20210117595 17/047405 |
Document ID | / |
Family ID | 1000005372409 |
Filed Date | 2021-04-22 |
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United States Patent
Application |
20210117595 |
Kind Code |
A1 |
DUAN; Libin ; et
al. |
April 22, 2021 |
SUBDOMAIN HYBRID CELLULAR AUTOMATA METHOD FOR SOLVING CAR BODY
THICKNESS OPTIMIZATION
Abstract
A subdomain hybrid cellular automata method for solving car body
thickness optimization includes an outer loop and an inner loop:
the outer loop is to conduct crash finite element simulation
analysis, calculate an output response, and update a cell internal
energy density, and update a target mass using a penalty function
method; the inner loop is mainly to adjust a cell thickness using a
PID control strategy according to internal energy densities of a
current cell and neighboring cells thereof, so that a current mass
of the inner loop converges to the target mass; and finally the
cell internal energy density distribution approaches a step target
internal energy density function as much as possible. Step target
internal energy density update rules are provided in the inner
loop. Cell thickness update rules based on a PID control strategy
are provided in the inner loop.
Inventors: |
DUAN; Libin; (Zhenjiang,
CN) ; LUO; Xin; (Zhenjiang, CN) ; JIANG;
Haobin; (Zhenjiang, CN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
JIANGSU UNIVERSITY |
Zhenjiang |
|
CN |
|
|
Assignee: |
JIANGSU UNIVERSITY
Zhenjiang
CN
|
Family ID: |
1000005372409 |
Appl. No.: |
17/047405 |
Filed: |
May 8, 2020 |
PCT Filed: |
May 8, 2020 |
PCT NO: |
PCT/CN2020/089175 |
371 Date: |
October 14, 2020 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06F 30/15 20200101;
G06F 2111/04 20200101; G06F 30/23 20200101 |
International
Class: |
G06F 30/23 20060101
G06F030/23; G06F 30/15 20060101 G06F030/15 |
Foreign Application Data
Date |
Code |
Application Number |
May 9, 2019 |
CN |
201910384617.0 |
May 6, 2020 |
CN |
202010373134.3 |
Claims
1. A subdomain hybrid cellular automata method for solving car body
thickness optimization, characterized by comprising the following
steps: S1. building an initially designed crash finite element
model for thickness optimization of a car body structure; S2.
building a subdomain cellular automata model for thickness
optimization of a car body structure, and defining thickness
variables and field variables; S3. executing an outer loop:
obtaining a cell internal energy density and a constraint function
value at a current design point through simulation analysis, and
updating a target mass using a penalty function method according to
an extent to which the current design point violates a constraint
boundary; S4. executing an inner loop: S4.1. constructing a step
target internal energy density function, and updating a target
internal energy density; a process of constructing the step target
internal energy density function is: S4.1.1. according to
subscripts i and j of a cell .OMEGA..sub.i,j, defining a sequence
number for the cell using id(i, j)={circumflex over
(N)}.sub..OMEGA..sub.i-1*(i-1)+j, j.di-elect cons.[1,
N.sub..OMEGA..sub.i], {circumflex over (N)}.sub..OMEGA..sub.0=0,
wherein {circumflex over (N)}.sub..OMEGA..sub.i-1 is the number of
cells in an (i-1)th subdomain; S4.1.2. traversing all cells, and
calculating a difference between internal energy densities
S.sub.id.sup.(k) of all cells and an average S.sup.(k) thereof in a
kth outer loop: .DELTA.S.sub.id.sup.(k)=S.sub.id.sup.(k)-S.sup.(k),
wherein S _ ( k ) = 1 i = 1 l N ^ .OMEGA. i i = 1 l j = 1 N ^
.OMEGA. i S .OMEGA. i , j ( k ) ##EQU00024## is the average of the
internal energy densities of all the cells in the kth outer loop;
S4.1.3. determining "step points" and "step ranges": traversing all
cells, and when
.DELTA.S.sub.id.sup.(k)*.DELTA.S.sub.id+1.sup.(k)<0 is
established, defining a subscript id of .DELTA.S.sub.id.sup.(k) as
a "step point," wherein m "step points" are capable of forming m+1
"step ranges"; S4.1.4. updating the "step points" and "step
ranges": if id.sub.i+1-id.sub.i+1<H.sub.threshold is
established, when i=1, deleting a "step point" id.sub.1, and a
"step range" is updated from [id.sub.0,id.sub.1] to
[id.sub.0,id.sub.2]; when i>1, deleting a "step point"
id.sub.i-1, and a "step range" is updated from
[id.sub.i-1,id.sub.i] to [id.sub.i-2,id.sub.i]; if
id.sub.i+1-id.sub.i+1<H.sub.threshold is not established,
retaining the original "step points" and "step ranges"; S4.1.5.
constructing the step target internal energy density function: S *
( h , k ) = { S 1 * ( h , k ) , 1 .ltoreq. i d .ltoreq. i d 1 S 2 *
( h , k ) , i d 1 < i d .ltoreq. i d 2 S i * ( h , k ) , i d i -
1 < i d .ltoreq. i d i S m ' * ( h , k ) , id m ' - 1 < i d
.ltoreq. i d m ' S m ' + 1 * ( h , k ) , id m ' < i d .ltoreq. i
= 1 l N ^ .OMEGA. i ##EQU00025## wherein S.sub.i*.sup.(h,k) is a
target internal energy density in the "step range"
[id.sub.i-1,id.sub.i] in the kth outer loop and an hth inner loop.
S4.2. updating a cell thickness using cell thickness update rules
based on a PID control strategy; S4.3. judging whether the inner
loop converges: if a convergence condition is not satisfied,
returning to S4.1; if the convergence condition is satisfied,
exiting the inner loop and performing S5; S5: judging whether the
outer loop converges: if global convergence conditions are not
satisfied, returning to S3 and updating the cell thickness using
the inner loop; if the global convergence conditions are satisfied,
outputting an optimization result.
2. The subdomain hybrid cellular automata method for solving car
body thickness optimization according to claim 1, characterized in
that the subdomains are subdomains in a discrete design space, and
a cellular automata model defined for each subdomain comprises a
current cell and neighboring cells thereof.
3. The subdomain hybrid cellular automata method for solving car
body thickness optimization according to claim 2, characterized in
that the cell type comprises one-dimensional cellular automata,
two-dimensional cellular automata, and three-dimensional cellular
automata.
4. The subdomain hybrid cellular automata method for solving car
body thickness optimization according to claim 1, characterized in
that a formula used in updating the target internal energy density
is: S i * ( h + 1 , k ) = S i * ( h , k ) M ( h , k ) M * ( k )
##EQU00026## wherein M*.sup.(k) represents a target mass obtained
by update in the kth outer loop; M.sup.(h,k) represents a current
mass obtained by thickness update in the kth outer loop and the hth
inner loop.
5. The subdomain hybrid cellular automata method for solving car
body thickness optimization according to claim 1, characterized in
that the cell thickness update rules based on the PID control
strategy are: a cell thickness update formula is: t .OMEGA. i , j (
h + 1 , k ) = { t .OMEGA. i , j min , t .OMEGA. i , j ( h , k ) +
.DELTA. t .OMEGA. i , j ( h , k ) < t .OMEGA. i , j min t
.OMEGA. i , j ( h , k ) + .DELTA. t .OMEGA. i , j ( h , k ) , t
.OMEGA. i , j min .ltoreq. t .OMEGA. i , j ( h , k ) + .DELTA. t
.OMEGA. i , j ( h , k ) .ltoreq. t .OMEGA. i , j max t .OMEGA. i ,
j max , t .OMEGA. i , j ( h , k ) + .DELTA. t .OMEGA. i , j ( h , k
) > t .OMEGA. i , j max ##EQU00027## in the formula,
t.sub..OMEGA..sub.i,j.sup.(h,k) is a cell thickness of a jth cell
in an ith subdomain .OMEGA..sub.i in the kth outer loop and the hth
inner loop; t.sub..OMEGA..sub.i,j.sup.(h+1,k) s a cell thickness of
the jth cell in the ith subdomain .OMEGA..sub.i in the kth outer
loop and an (h+1)th inner loop; t.sub..OMEGA..sub.i,j.sup.min and
t.sub..OMEGA..sub.i,j.sup.max are respectively a minimum and a
maximum of the cell thickness of the jth cell in the ith subdomain
.OMEGA..sub.i; .DELTA..sub..OMEGA..sub.i,j.sup.(h,k) is a variation
of the cell thickness of the jth cell in the ith subdomain
.OMEGA..sub.i in the kth outer loop and the hth inner loop, and has
an expression as follows:
.DELTA.t.sub..OMEGA..sub.i,j.sup.(h,k)=(t.sub..OMEGA..sub.i,j.sup.max-t.s-
ub..OMEGA..sub.i,j.sup.min)f(e.sub..OMEGA..sub.i,j.sup.(h,k))
wherein f(e.sub..OMEGA..sub.i,j.sup.(h,k)) is a PID control
function for cell thickness update, and has an expression as
follows: f ( e .OMEGA. i , j ( h , k ) ) = K p e .OMEGA. i , j ( h
, k ) + K i [ e .OMEGA. i , j ( h , k ) + .tau. = 1 k - 1 e .OMEGA.
i , j ( .tau. ) ] + K d .times. [ e .OMEGA. i , j ( h , k ) - e
.OMEGA. i , j ( k - 1 ) ] ##EQU00028## wherein K.sub.p is a
proportional control coefficient, K.sub.i is an integral control
coefficient, K.sub.d is a differential control coefficient,
e.sub..OMEGA..sub.i,j.sup.(.tau.) represents a relative deviation
item of a .tau. th outer loop, e.sub..OMEGA..sub.i,j.sup.(k-1)
represents a relative deviation item of a (k-1)th outer loop, and
e.sub..OMEGA..sub.i,j.sup.(h,k) represents a relative deviation
item between an internal energy density
S.sub..OMEGA..sub.i,j.sup.(k) of the current cell and a target
internal energy density S.sub.m'*.sup.(h,k) and has a calculation
formula as follows: e .OMEGA. i , j ( h , k ) = S .OMEGA. i , j ( k
) - S m ' * ( h , k ) S m ' * ( h , k ) , ##EQU00029##
6. The subdomain hybrid cellular automata method for solving car
body thickness optimization according to claim 1, characterized in
that the convergence condition of the inner loop is:
|M.sup.(h,k)-M*.sup.(k)|<.epsilon..sub.1 or
k.sub.1.gtoreq.k.sub.lmax, wherein M*.sup.(k) represents a target
mass obtained by update in the kth outer loop; M.sup.(h,k)
represents a current mass obtained by thickness update in the kth
outer loop and the hth inner loop, .epsilon..sub.1 is a mass
convergence factor, k.sub.1 represents the number of iterations in
the inner loop, and k.sub.1max represents the maximum number of
iterations in the inner loop.
7. The subdomain hybrid cellular automata method for solving car
body thickness optimization according to claim 1, characterized in
that the global convergence conditions comprise: (1) when the
number of iterations k in the outer loop exceeds a predefined
maximum number of iterations k.sub.max, ending iteration; (2) let
p.sub.f represent the number of iterations where infeasible
solutions continuously appear, and p*.sub.f represent the maximum
number of iterations where infeasible solutions continuously
appear; when p.sub.f>p*.sub.f, ending iteration; (3) when the
variation of design variables satisfies i = 1 N t .OMEGA. i , j k -
t .OMEGA. i , j k - 1 < 2 , ##EQU00030## ending iteration; in
the formula, N represents the total number of cells, and
.epsilon..sub.2 represents a global convergence factor.
Description
CROSS REFERENCE TO THE RELATED APPLICATIONS
[0001] This application is the national phase entry of
International Application No. PCT/CN2020/089175, filed on May 8,
2020, which is based upon and claims priority to Chinese Patent
Application No. 201910384617.0, filed on May 9, 2019, and Chinese
Patent Application No. 202010373134.3, filed on May 6, 2020, the
entire contents of which are incorporated herein by reference.
TECHNICAL FIELD
[0002] The present invention relates to the technical field of
crashworthiness optimization for car body structures, and
specifically to a subdomain hybrid cellular automata method for
solving car body thickness optimization.
BACKGROUND
[0003] Finite element simulation of vehicle crash involves material
nonlinearity, geometric nonlinearity, and contact boundary
nonlinearity, and is a typical dynamic nonlinear analysis problem.
In order to obtain desirable vehicle safety performance,
crashworthiness optimization design for car body structures has
been widely applied in the vehicle industry. Since the output
response of crash simulation has numerical noise and physical
oscillation phenomena, a gradient-based optimization algorithm
cannot effectively solve crashworthiness optimization problems for
car body structures. In addition, a full-scale vehicle crash
simulation requires a lot of computation time, and an evolutionary
algorithm usually requires thousands of finite element simulation
analyses, resulting in lengthy optimization. A surrogate
model-based numerical optimization method is the main way to solve
the aforementioned problems, and classical algorithms include PSP
algorithm, parallel EGO algorithm based on pseudo EI criterion, and
so on. However, when a large number of (for example, 30 or even
more) design variables exist, the optimization efficiency of most
surrogate model-based optimization algorithms is greatly
reduced.
[0004] A hybrid cellular automata (HCA) method, as a non-gradient
heuristic algorithm, has the following advantages for solving
crashworthiness optimization problems for thin-walled structures:
1) gradient information does not need to be calculated in the
optimization process, which has a great advantage in solving
complex nonlinear optimization problems where sensitivity
information is hard to obtain: 2) the crashworthiness performance
of the structures can be rapidly improved without requiring a large
number of finite element simulations; 3) the optimization problem
with a large scale of design variables can be solved without
significantly increasing the computation time.
[0005] The car body is a three-dimensional space frame structure
formed by a large number of thin-walled structures, and the
crashworthiness optimization design for a car body structure is a
typical nonlinear dynamic response optimization problem in a
discrete design space, and such problems usually involve thickness
design variables of a large number of different parts.
[0006] Efficient methods for solving a nonlinear dynamic response
optimization problem with a large scale of thickness variables in a
discrete design space are limited in the existing research.
SUMMARY
[0007] In view of the deficiencies in the prior art, the present
invention provides a subdomain hybrid cellular automata method for
solving car body thickness optimization (Thickness-based Subdomain
Hybrid Cellular Automata, T-Subdomain HCA), which can efficiently
solve a nonlinear dynamic response optimization problem with a
large scale of thickness variables.
[0008] The present invention achieves the aforementioned technical
objective by the following technical means.
[0009] A subdomain hybrid cellular automata method (T-Subdomain
HCA) for solving car body thickness optimization includes the
following steps:
[0010] S1. building an initially designed crash finite element
model for thickness optimization of acar body structure;
[0011] S2. building a subdomain cellular automata model for
thickness optimization of a car body structure, and defining
thickness variables and field variables;
[0012] S3. executing an outer loop: obtaining a cell internal
energy density and a constraint function value at a current design
point through simulation analysis, and updating a target mass using
a penalty function method according to an extent to which the
current design point violates a constraint boundary;
[0013] S4. executing an inner loop:
[0014] S4.1. constructing a step target internal energy density
function, and updating target internal energy density;
[0015] S4.2. updating cell thicknesses using cell thickness update
rules based on a PID control strategy;
[0016] S4.3. judging whether the inner loop converges: if a
convergence condition is not satisfied, returning to S4.1; if the
convergence condition is satisfied, exiting the inner loop and
performing S5;
[0017] S5: judging whether the outer loop converges: if global
convergence conditions are not satisfied, returning to S3 and
updating the cell thicknesses using the inner loop; if the global
convergence conditions are satisfied, outputting an optimization
result.
[0018] Further, the subdomains are subdomains in a discrete design
space, and a cellular automata model defined for each subdomain
includes a current cell and neighboring cells thereof.
[0019] Furthermore, the cell type includes one-dimensional cellular
automata, two-dimensional cellular automata, and three-dimensional
cellular automata.
[0020] Further, a process of constructing the step target internal
energy density function is:
[0021] S4.1.1. according to subscripts i and j of a cell
.OMEGA..sub.i,j, defining a sequence number for the cell using id
(i, j)={circumflex over (N)}.sub..OMEGA..sub.i-1*(i-1)+j,
j.di-elect cons.[1, {circumflex over (N)}.sub..OMEGA..sub.i],
{circumflex over (N)}.sub..OMEGA..sub.0, =0, where {circumflex over
(N)}.sub..OMEGA..sub.i-1 is the number of cells in an (i-1)th
subdomain;
[0022] S4.1.2. traversing all cells, and calculating a difference
between internal energy densities S.sub.id.sup.(k) of all cells and
an average S.sup.(k) thereof in a kth outer loop:
.DELTA.S.sub.id.sup.(k)=S.sub.id.sup.(k)-S.sup.(k), where
S ( k ) = 1 i = 1 l N ^ .OMEGA. i i = 1 l j = 1 N ^ .alpha. i S
.OMEGA. i , j ( k ) ##EQU00001##
is the average of the internal energy densities of all cells in the
kth outer loop;
[0023] S4.1.3. determining "step points" and "step intervals":
traversing all cells, and when
.DELTA.S.sub.id.sup.(k)*.DELTA.S.sub.id+1.sup.(k)<0 is
established, defining a subscript id of .DELTA.S.sub.id.sup.(k) as
a "step point," where m "step points" are capable of forming m+1
"step intervals";
[0024] S4.1.4. updating the "step points" and "step intervals": if
id.sub.i+1-id.sub.i+1<H.sub.threshod is established, when i=1,
deleting a "step point" id.sub.1, and a "step interval" is updated
from [id.sub.0,id.sub.1] to [id.sub.0,id.sub.2]; when i>1,
deleting a "step point" id.sub.i-1, and a "step interval" is
updated from [id.sub.i-1,id.sub.i] to [id.sub.i-2,id.sub.i]; if
id.sub.i+1-id.sub.i+1<H.sub.threshold is not established,
retaining the original "step points" and "step intervals";
[0025] S4.1.5. constructing the step target internal energy density
function:
S * ( h , k ) = { S 1 * ( h , k ) , 1 .ltoreq. id .ltoreq. id 1 S 2
* ( h , k ) , id 1 < id .ltoreq. id 2 S i * ( h , k ) , id i - 1
< id .ltoreq. id i S m ' * ( h , k ) , id m ' - 1 < id
.ltoreq. id m ' S m ' + 1 * ( h , k ) , id m ' < id .ltoreq. i =
1 l N ^ .OMEGA. i ##EQU00002##
[0026] where S.sub.i*.sup.(h,k) is a target internal energy density
in the "step interval" [id.sub.i-1,id.sub.i] in the kth outer loop
and an hth inner loop.
[0027] Furthermore, a formula used in updating the target internal
energy density is:
S i * ( h + 1 , k ) = S i * ( h , k ) M ( h , k ) M * ( k )
##EQU00003##
[0028] where M*.sup.(k) represents a target mass obtained by update
in the kth outer loop; M.sup.(h,k) represents a current mass
obtained by thickness update in the kth outer loop and the hth
inner loop.
[0029] Further, the cell thickness update rules based on the PID
control strategy are:
[0030] a cell thickness update formula is:
t .OMEGA. i , j ( h + 1 , k ) = { t .OMEGA. i , j m i n , t .OMEGA.
i , j ( h , k ) + .DELTA. t .OMEGA. i , j ( h , k ) < t .OMEGA.
i , j m i n t .OMEGA. i , j ( h , k ) + .DELTA. t .OMEGA. i , j ( h
, k ) , t .OMEGA. i , j m i n .ltoreq. t .OMEGA. i , j ( h , k ) +
.DELTA. t .OMEGA. i , j ( h , k ) .ltoreq. t .OMEGA. i , j m ax t
.OMEGA. i , j ma x , t .OMEGA. i , j ( h , k ) + .DELTA. t .OMEGA.
i , j ( h , k ) > t .OMEGA. i , j ma x ##EQU00004##
[0031] in the formula, t.sub..OMEGA..sub.i,j.sup.(h,k) is a cell
thickness of a jth cell in an ith subdomain .OMEGA..sub.i in the
kth outer loop and the hth inner loop;
t.sub..OMEGA..sub.i,j.sup.(h+1,k) is a cell thickness of the jth
cell in the ith subdomain .OMEGA..sub.i in the kth outer loop and
an (h+1)th inner loop; t.sub..OMEGA..sub.i,j.sup.min and
t.sub..OMEGA..sub.i,j.sup.max are respectively a minimum and a
maximum of the cell thickness of the jth cell in the ith subdomain
.OMEGA..sub.i; .DELTA.t.sub..OMEGA..sub.i,j.sup.(h,k) is a
variation of the cell thickness of thejth cell in the ith subdomain
.OMEGA..sub.i in the kth outer loop and the hth inner loop, and has
an expression as follows:
.DELTA.t.sub..OMEGA..sub.i,j.sup.(h,k)=(t.sub..OMEGA..sub.i,j.sup.max-t.-
sub..OMEGA..sub.i,j.sup.min)f(e.sub..OMEGA..sub.i,j.sup.(h,k))
where f(e.sub..OMEGA..sub.i,j.sup.(h,k)) is a PID control function
for cell thickness update, and has an expression as follows:
f ( e .OMEGA. i , j ( h , k ) ) = K p e .OMEGA. i , j ( h , k ) + K
i [ e .OMEGA. i , j ( h , k ) + .tau. = 1 k - 1 e .OMEGA. i , j (
.tau. ) ] + K d .times. [ e .OMEGA. i , j ( h , k ) - e .OMEGA. i ,
j ( k - 1 ) ] ##EQU00005##
[0032] where K.sub.p is a proportional control coefficient, K.sub.i
is an integral control coefficient, K.sub.d is a differential
control coefficient, e.sub..OMEGA..sub.i,j.sup.(.tau.) represents a
relative deviation item of a .tau.th outer loop,
e.sub..OMEGA..sub.i,j.sup.(k-1) represents a relative deviation
item of a (k-1)th outer loop, and e.sub..OMEGA..sub.i,j.sup.(h,k)
represents a relative deviation item between an internal energy
density S.sub..OMEGA..sub.i,j.sup.(k), of the current cell and a
target internal energy density S.sub.m'*.sup.(h,k), and has a
calculation formula as follows:
e .OMEGA. i , j ( h , k ) = S .OMEGA. i , j ( k ) - S m ' * ( h , k
) S m ' * ( h , k ) . ##EQU00006##
Further, the convergence condition of the inner loop is:
|M.sup.(h,k)-M*.sup.(k)|<.epsilon..sub.1 or
k.sub.1.gtoreq.k.sub.1max, where M*.sup.(k) represents a target
mass obtained by update in the kth outer loop; M.sup.(h,k)
represents a current mass obtained by thickness update in the kth
outer loop and the hth inner loop, .epsilon..sub.1 is a mass
convergence factor, k.sub.1 represents the number of iterations in
the inner loop, and k.sub.1max represents the maximum number of
iterations in the inner loop.
[0033] Further, the global convergence conditions include:
[0034] (1) when the number of iterations k in the outer loop
exceeds a predefined maximum number of iterations k.sub.max, ending
iteration;
[0035] (2) let p.sub.f represent the number of iterations where
infeasible solutions continuously appear, and P*.sub.f represent
the maximum number of iterations where infeasible solutions
continuously appear; when p.sub.f>p.sub.f*, ending
iteration;
[0036] (3) when the variation of design variables satisfies
i = 1 N t .OMEGA. i , j k - t .OMEGA. i , j k - 1 < 2 ,
##EQU00007##
ending iteration; in the formula, N represents the total number of
cells, and .epsilon..sub.2 represents a global convergence
factor.
[0037] The present invention has the following beneficial
effects:
[0038] (1) the subdomain CA model of the present invention allows
defining different types of cellular automata models
CA.sub..OMEGA..sub.i in different subdomains, and allows using
different types of cell state update rules R.sub..OMEGA..sub.i in
different subdomains, so that the hybrid cellular automata method
can solve one-dimensional, two-dimensional, and three-dimensional
nonlinear dynamic structural optimization problems and any
combination thereof in a discrete design space.
[0039] (2) A step target internal energy density function is used
in the inner loop of the present invention, so that the global
optimal solution search capability of the hybrid cellular automata
method can be effectively improved.
[0040] (3) Cell thickness update rules based on a PID control
strategy are used in the inner loop of the present invention, so
that the robustness of the hybrid cellular automata method can be
effectively improved.
[0041] (4) Gradient information does not need to be calculated in
the optimization process of the present invention, which has a
great advantage in solving complex nonlinear problems where
sensitivity information is hard to obtain.
BRIEF DESCRIPTION OF THE DRAWINGS
[0042] FIG. 1 is a flowchart of a subdomain hybrid cellular
automata method for solving car body thickness optimization in the
present invention;
[0043] FIG. 2 is a schematic diagram of a subdomain CA model in the
present invention;
[0044] FIG. 3 is a schematic diagram of a two-dimensional subdomain
CA model in the present invention;
[0045] FIGS. 4A-4B are schematic diagrams of a step target internal
energy density function in the present invention, where FIG. 4A is
a schematic diagram of a step target internal energy density
function when H.sub.threshold=0 and V.sub.threshold=1, and FIG. 4B
is a schematic diagram of the step target internal energy density
function when H.sub.threshold=3 and V.sub.threshold=1.1;
[0046] FIG. 5 is a schematic diagram of a full-vehicle side crash
finite element model in the present invention;
[0047] FIG. 6 is a schematic diagram of a subdomain CA model of a
car body beam framework in the present invention;
[0048] FIGS. 7A-7C are curve diagrams of iteration processes of a
T-Subdomain HCA #1 algorithm in the present invention, where FIG.
7A is a diagram illustrating a mass convergence curve of the
T-Subdomain HCA #1 algorithm in the present invention, FIG. 7B is a
diagram of an iteration process with a maximum intrusion amount of
the T-Subdomain HCA #1 algorithm in the present invention, and FIG.
7C is a diagram of an iteration process with a maximum intrusion
velocity of the T-Subdomain HCA #1 algorithm in the present
invention;
[0049] FIGS. 8A-8C are curve diagrams of iteration processes of a
T-Subdomain HCA #2 algorithm in the present invention, where FIG.
8A is a diagram illustrating a mass convergence curve of the
T-Subdomain HCA #2 algorithm in the present invention, FIG. 8B is a
diagram of an iteration process with a maximum intrusion amount of
the T-Subdomain HCA #2 algorithm in the present invention, and FIG.
8C is a diagram of an iteration process with a maximum intrusion
velocity of the T-Subdomain HCA #2 algorithm in the present
invention;
[0050] FIGS. 9A-9C are curve diagrams of iteration processes of a
parallel EGO-PCEI algorithm in the present invention, where FIG. 9A
is a diagram illustrating a mass convergence curve of the parallel
EGO-PCEI algorithm in the present invention, FIG. 9B is a diagram
of an iteration process with a maximum intrusion amount of the
parallel EGO-PCEI algorithm in the present invention, and FIG. 9C
is a diagram of an iteration process with a maximum intrusion
velocity of the parallel EGO-PCEI algorithm in the present
invention;
[0051] FIGS. 10A-10B are comparison diagrams of intrusion amount
curves before and after optimization in the present invention,
where FIG. 10A is a comparison diagram of intrusion amount curves
at a B-pillar waistline location before and after optimization in
the present invention, and FIG. 10B is a comparison diagram of
intrusion amount curves at a B-pillar pelvis location before and
after optimization in the present invention;
[0052] FIGS. 11A-11B are comparison diagrams of intrusion velocity
curves before and after optimization in the present invention,
where FIG. 11A is a comparison diagram of intrusion velocity curves
at a B-pillar waistline location before and after optimization in
the present invention, and FIG. 11B is a comparison diagram of
intrusion velocity curves at a B-pillar pelvis location before and
after optimization in the present invention; and
[0053] FIGS. 12A-12B are comparison diagrams of car body
deformation patterns before and after optimization in the present
invention, where FIG. 12A is a diagram of a car body deformation
pattern before optimization in the present invention, and FIG. 12B
is a diagram of a car body deformation pattern after optimization
in the present invention.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[0054] The present invention is further illustrated below with
reference to the accompanying drawings and specific embodiments,
but the protection scope of the present invention is not limited
thereto.
[0055] A subdomain hybrid cellular automata method for solving car
body thickness optimization (Thickness-based Subdomain Hybrid
Cellular Automata, T-Subdomain HCA) includes an outer loop and an
inner loop: the outer loop is mainly to conduct finite element
simulation analysis, calculate an output response and a cell
internal energy density, and define an appropriate target mass for
the inner loop to achieve minimization of a structural mass under
performance constraints; the inner loop is to update a step target
internal energy density function according to the target mass and
the internal energy density distribution, and then update a cell
thickness according to a PID control strategy, so that a current
mass of the inner loop converges to the target mass; and finally
the cell internal energy density distribution approaches the step
target internal energy density function as much as possible.
[0056] As shown in FIG. 1, a subdomain hybrid cellular automata
method for solving car body thickness optimization specifically
includes the following steps:
[0057] S1. an initially designed crash finite element model for
thickness optimization of a car body structure is built.
[0058] Finite element preprocessing software is used to divide a
full-vehicle geometric model into finite element meshes, and then
assign attributes and materials thereto, and complete model
assembly, connection and boundary condition definition; a
full-vehicle crash finite element model is established according to
the above steps.
[0059] S2. A subdomain cellular automata model for thickness
optimization of a car body structure is built, and thickness
variables (namely, part thicknesses) and field variables (namely,
part internal energy densities) are defined.
[0060] For a nonlinear dynamic response structural optimization
problem with a large scale of design variables in a discrete design
space, the concept of "subdomain CA model" is introduced based on a
conventional cellular automata model (Cellular Automata, CA), the
discrete design space is divided into l subdomains, and a rational
cellular automata model is defined for each subdomain, as shown in
FIG. 2. Assume that a global design space .OMEGA. consists of l
discrete subdomains .OMEGA..sub.i (i=1, 2,L, l), and each subdomain
.OMEGA..sub.i is described by a cellular automata model
CA.sub..OMEGA..sub.i and a cell state .alpha..sub..OMEGA..sub.i,
and the corresponding mathematical expression is:
Q(CA.sub..OMEGA.,.alpha..sub..OMEGA.)=.OMEGA..sub.1(CA.sub..OMEGA..sub.1-
,.alpha..sub..OMEGA..sub.1)+.OMEGA..sub.2(CA.sub..OMEGA..sub.2,.alpha..sub-
..OMEGA.2)+L+.OMEGA..sub.i(CA.sub..OMEGA..sub.i,.alpha..sub..OMEGA..sub.i)-
+L+.OMEGA..sub.i(CA.sub..OMEGA..sub.i,.alpha..sub..OMEGA..sub.i)
(1)
[0061] where .OMEGA..sub.i is an ith subdomain in the global design
space .OMEGA., CA.sub..OMEGA..sub.i is a cellular automata model
(consisting of a current cell and neighboring cells thereof, where
the cell type includes one-dimensional cellular automata,
two-dimensional cellular automata, and three-dimensional cellular
automata) of the ith subdomain, and a. is a cell state of the ith
subdomain.
[0062] A jth cell state .alpha..sub..OMEGA..sub.i,j in the ith
subdomain .OMEGA..sub.i in FIG. 2 may be represented as:
.alpha. .OMEGA. i , j = { t .OMEGA. i , j S .OMEGA. i , j } ( 2 )
##EQU00008##
[0063] in the formula, t.sub..OMEGA..sub.i,j and
S.sub..OMEGA..sub.i,j, are respectively a thickness variable (for
example, a part thickness or a unit thickness) and a field variable
(for example, an internal energy density) of a jth cell in the ith
subdomain .OMEGA..sub.i. A calculation formula of the field
variable S.sub..OMEGA..sub.i,j is:
S .OMEGA. = 1 N ^ .OMEGA. i , j + 1 n .di-elect cons. N .OMEGA. i ,
j U .OMEGA. i , n t .OMEGA. i , n A .OMEGA. i , n ( 3 )
##EQU00009##
[0064] in the formula, U.sub..OMEGA..sub.i,n is internal energy of
an nth cell in the ith subdomain Q.sub.t; t.sub..OMEGA..sub.i,n and
A.sub..OMEGA..sub.i,n are respectively a thickness and a surface
area of the nth cell in the ith subdomain .OMEGA..sub.i;
N.sub..OMEGA..sub.i,n is a set of the neighboring cells of the jth
cell in the ith subdomain .OMEGA..sub.i, and the number of the
cells in the collection is {circumflex over
(N)}.sub..OMEGA..sub.i,j; S.sub..OMEGA..sub.i,n is a local internal
energy density of the jth cell in the ith subdomain .OMEGA..sub.i,
namely, the field variable.
[0065] A specific example of a subdomain CA model defined in a
two-dimensional discrete design space is as follows. The discrete
design space .OMEGA. in FIG. 3 consists of four subdomains (namely,
.OMEGA..sub.1, .OMEGA..sub.2, .OMEGA..sub.3, and .OMEGA..sub.4); a
cell type of the subdomain .OMEGA..sub.1 is empty type, and the
number of neighboring cells of the current cell is 0; a cell type
of the subdomain .OMEGA..sub.2 is Von Neumann type, and the number
of neighboring cells of the current cell is 4; a cell type of the
subdomain .OMEGA..sub.3 is Moore type, and the number of
neighboring cells of the current cell is 8; a cell type of the
subdomain .OMEGA..sub.4 is Margolus type, and the number of
neighboring cells of the current cell is 24.
[0066] S3. The process enters an outer loop, and the following
steps are performed:
[0067] S3.1. simulation software such as LS DYNA or Radioss or
Abaqus or Ansys is invoked to conduct nonlinear dynamic crash
simulation analysis, and a cell internal energy density and a
constraint function value at a current design point are obtained
according to a result of the simulation analysis;
[0068] S3.2. a target mass is updated using a penalty function
method according to an extent to which the current design point
violates a constraint boundary.
[0069] A target mass penalty .DELTA.M*.sup.(k) is used to represent
the extent to which the current design point violates the
constraint boundary in a kth outer loop and then update a target
mass M*.sup.(k) in the kth outer loop.
[0070] The specific expression of the target mass penalty
.DELTA.M*.sup.(k) is:
.DELTA. M * ( k ) = min ( max ( K q M * ( 0 ) .delta. ( k ) , -
.DELTA. M ) , .DELTA. M ) ( 4 ) .delta. ( k ) = i = 1 n g O i ( k )
- O i * O i * ( 5 ) ##EQU00010##
[0071] where n.sub.g is the number of constraint functions; K.sub.q
represents a proportionality coefficient of the target mass
penalty; O.sub.i.sup.(k) is a response value of an ith constraint
function in the kth outer loop, O.sub.i* is a constraint boundary
of the ith constraint function; .delta..sup.(k) represents relative
deviation items between n.sub.g constraint functions and constraint
boundaries thereof; M*.sup.(0) represents an initial total weight
of the structure in the design space, and .DELTA.M represent a
maximum penalty of the target mass.
[0072] Therefore, an update formula for the target mass M*.sup.(k)
in the kth outer loop is:
M*.sup.(k)=min(M*.sup.(k-1)+.DELTA.M*.sup.(k)M*.sup.(k')) (6)
[0073] where k' represents the location of a most recent feasible
solution in the number of iterations in the outer loop; if the
iterative outer loop has no feasible solution till now, k'=0.
[0074] S4. The process enters an inner loop, and the following
steps are performed:
[0075] S4.1. a step target internal energy density function (step
IED target, SIED*) is constructed, and a target internal energy
density is updated.
[0076] In order to effectively improve the search capability for a
global optimal solution of a T-Subdomain HCA algorithm, the present
invention provides a step target internal energy density update
function, where the construction process and update rules of the
step target internal energy density function are as follows:
[0077] S4.1.1. cell sequence number definition: a cell neighborhood
relationship in each subdomain is kept unchanged, and according to
subscripts i and j of the cell .OMEGA..sub.i,j, a sequence number
id is defined for the cell using formula (7), that is, id is a
function about the subscripts i and j of the cell .OMEGA..sub.i,j,
and then S.sub.id(i,j).sup.(k)=S.sub..OMEGA..sub.i,j.sup.(k);
id(i,j)={circumflex over
(N)}.sub..OMEGA..sub.i-1*(i-1)+j,j.di-elect
cons.[1,N.sub..OMEGA..sub.i],N.sub..OMEGA..sub.0=0 (7) [0078] where
{circumflex over (N)}.sub..OMEGA..sub.i-1 is the number of cells in
an (i-1)th subdomain.
[0079] S4.1.2. All cells are traversed, and a difference between
internal energy densities S.sub.id.sup.(k) of all cells and an
average S.sup.(k) thereof in the kth outer loop is calculated:
.DELTA.S.sub.id.sup.(k)=S.sub.id.sup.(k)-S.sup.(k) (8)
[0080] where
S _ ( k ) = 1 i = 1 l N ^ .OMEGA. i i = 1 l j = 1 N ^ .OMEGA. i S
.OMEGA. i , j ( k ) ##EQU00011##
is the average of the internal energy densities of all the cells in
the kth outer loop.
[0081] S4.1.3. "Step points" and "step intervals" are
determined.
[0082] All the cells are traversed, and it is judged whether
formula (9) is established. If formula (9) is established, a
subscript id of .DELTA.S.sub.id.sup.(k) is defined as a "step
point" and denoted as id.sub.i. Assuming that m "step points" are
determined according to formula (9), the m "step points" can form
m+1 "step intervals" denoted as [id.sub.i-1,id.sub.i], where i=1, .
. . , m+1, id.sub.0
id m + 1 = i = 1 l N ^ .OMEGA. i . ##EQU00012##
.DELTA.S.sub.id.sup.(k)*.DELTA.S.sub.id+1.sup.(k)<0 (9)
[0083] S4.1.4. The "step points" and "step intervals" are
updated.
[0084] Let a width threshold of the "step interval" be
H.sub.threshold, all "step intervals" are traversed, and it is
judged whether formula (10) is established. If formula (10) is
established (that is, the "step interval" [id.sub.i-1,id.sub.i] has
a small width), the "step points" are deleted and the "step
intervals" are updated in the following manner: when i=1, a "step
point" id.sub.1 is deleted, the "step interval" is updated from
[id.sub.0,id.sub.1] to [id.sub.0,id.sub.2]; when i>1, a "step
point" id.sub.i-1 is deleted, and the "step interval" is updated
from [id.sub.i-1,id.sub.i] to [id.sub.i-2,id.sub.i]. If formula
(10) is not established, the original "step points" and "step
intervals" are retained. Assuming that the number of the updated
"step points" is m', the number of the updated "step intervals" is
m'+1.
id.sub.i+1-id.sub.i+1<H.sub.threshold (10)
[0085] S4.1.5. The step target internal energy density function is
constructed, and the equation is as follows:
S * ( h , k ) = { S 1 * ( h , k ) , 1 .ltoreq. id .ltoreq. id 1 S 2
* ( h , k ) , id 1 < id .ltoreq. id 2 S i * ( h , k ) , id i - 1
< id .ltoreq. id i S m ' * ( h , k ) , id m ' - 1 < id
.ltoreq. id m ' S m ' + 1 * ( h , k ) , id m ' < id .ltoreq. i =
1 l N ^ .OMEGA. i ( 11 ) ##EQU00013##
[0086] where S.sub.i*.sup.(h,k) is a target internal energy density
in the "step interval" [id.sub.i-1,id.sub.i] in the kth outer loop
and an hth inner loop.
[0087] S4.1.6. The step target internal energy density function is
updated: in order to achieve the specified target mass in the outer
loop, a target internal energy density of each "step interval" in
the inner loop is updated according to formula (12).
S i * ( h + 1 , k ) = S i * ( h , k ) M ( h , k ) M * ( k ) ( 12 )
##EQU00014##
[0088] where M*.sup.(k) represents the target mass obtained by
update in the kth outer loop; M.sup.(h,k) represents a current mass
obtained by thickness update in the kth outer loop and the hth
inner loop; an initial target internal energy density
S.sub.i*.sup.(0,k) of each "step interval" each time the process
enters the inner loop is obtained from formula (13):
S i * ( 0 , k ) = { S _ i ( k ) , S _ i ( k ) .gtoreq. S _ ( k ) *
V threshold S _ ( k ) , S _ i ( k ) < S _ ( k ) * V threshold (
13 ) ##EQU00015##
[0089] where V.sub.threshold is a target internal energy density
threshold coefficient in the "step interval"; S.sup.(k) is the
average of the internal energy densities of all the cells in the
kth outer loop; S.sub.i.sup.(k), is an average of internal energy
densities of all cells in the "step interval" [id.sub.i-i,id.sub.i]
(i=1, . . . , m+1), as shown in formula (14).
S _ i ( k ) = 1 i d i + 1 - id i + 1 i ' = id i i d i + 1 S i ' ( k
) ( 14 ) ##EQU00016##
[0090] When H.sub.threshold=0 and V.sub.threshold=1, a schematic
diagram of the step target internal energy density function
constructed according to the above step is shown in FIG. 4A; when
H.sub.threshold=3 and V.sub.threshold=1.1, a schematic diagram of
the step target internal energy density function constructed
according to the above step is shown in FIG. 4B; in the figures,
HIED* is a horizontal IED target, a horizontal target internal
energy density function step IED target, SIED*.
[0091] S4.2. a cell thickness is updated using cell thickness
update rules based on a PID control strategy.
[0092] In order to effectively improve the robustness of the
T-Subdomain HCA algorithm, the present invention provides cell
thickness update rules based on a PID control strategy. The cell
thickness update formula is:
t .OMEGA. i , j ( h + 1 , k ) = { t .OMEGA. i , j min , t .OMEGA. i
, j ( h , k ) + .DELTA. t .OMEGA. i , j ( h , k ) < t .OMEGA. i
, j min t .OMEGA. i , j ( h , k ) + .DELTA. t .OMEGA. i , j ( h , k
) , t .OMEGA. i , j min .ltoreq. t .OMEGA. i , j ( h , k ) +
.DELTA. t .OMEGA. i , j ( h , k ) .ltoreq. t .OMEGA. i , j max t
.OMEGA. i , j max , t .OMEGA. i , j ( h , k ) + .DELTA. t .OMEGA. i
, j ( h , k ) > t .OMEGA. i , j max ( 15 ) ##EQU00017##
[0093] in the formula, t.sub..OMEGA..sub.i,j.sup.(h,k) is a cell
thickness of the jth cell in the ith subdomain .OMEGA..sub.i in the
kth outer loop and the hth inner loop;
t.sub..OMEGA..sub.i,j.sup.(h+1,k) is a cell thickness of the jth
cell in the ith subdomain .OMEGA..sub.i in the kth outer loop and
an (h+1)th inner loop; t.sub..OMEGA..sub.i,j.sup.min and
t.sub..OMEGA..sub.i,j.sup.max are respectively a minimum and a
maximum of the cell thickness of the jth cell in the ith subdomain
Q.sub.i; .DELTA.t.sub..OMEGA..sub.i,j.sup.(h,k) is a variation of
the cell thickness of the jth cell in the ith subdomain
.OMEGA..sub.i in the kth outer loop and the hth inner loop, and has
an expression as follows:
.DELTA.t.sub..OMEGA..sub.i,j.sup.(h,k)=(t.sub..OMEGA..sub.i,j.sup.max-t.-
sub..OMEGA..sub.i,j.sup.min)f(e.sub..OMEGA..sub.i,j.sup.(h,k))
(16)
where f(et.sub..OMEGA..sub.i,j.sup.(h,k)) is a PID control function
for cell thickness update, and has an expression as follows:
f ( e .OMEGA. i , j ( h , k ) ) = K p e .OMEGA. i , j ( h , k ) + K
i [ e .OMEGA. i , j ( h , k ) + .tau. = 1 k - 1 e .OMEGA. i , j (
.tau. ) ] + K d .times. [ e .OMEGA. i , j ( h , k ) - e .OMEGA. i ,
j ( k - 1 ) ] ( 17 ) ##EQU00018##
[0094] where K.sub.p is a proportional control coefficient, K.sub.i
is an integral control coefficient, K.sub.d is a differential
control coefficient, et.sub..OMEGA..sub.i,j.sup.(.tau.) represents
a relative deviation item of a .tau.th outer loop,
et.sub..OMEGA..sub.i,j.sup.(k-1) represents a relative deviation
item of a (k-1)th outer loop, and et.sub..OMEGA..sub.i,j.sup.(h,k)
represents a relative deviation item between an internal energy
density S.sub..OMEGA..sub.i,j.sup.(k) of the current cell and a
target internal energy density S.sub.m'*.sup.(h,k), and has a
calculation formula as follows:
e .OMEGA. i , j ( h , k ) = S .OMEGA. i , j ( k ) - S m ' * ( h , k
) S m ' * ( h , k ) ( 18 ) ##EQU00019##
[0095] S4.3. it is judged whether the inner loop converges: if a
convergence condition for the inner loop is not satisfied, the
process returns to S4.1; if the convergence condition for the inner
loop is satisfied, the process exits the inner loop and S5 is
performed.
[0096] The convergence condition for the inner loop is:
M ( h , k ) - M * ( k ) < 1 or k 1 .gtoreq. k 1 max ( 19 )
##EQU00020##
[0097] in the formula, .epsilon..sub.1 is a mass convergence
factor, k.sub.1 represents the number of iterations in the inner
loop, and k.sub.1max represents the maximum number of iterations in
the inner loop.
[0098] S5: it is judged whether the outer loop converges: if global
convergence conditions for the outer loop are not satisfied, the
cell thickness is updated using the inner loop and the process
returns to S3; if the global convergence conditions are reached,
the T-Subdomain HCA algorithm converges and an optimization result
is output.
[0099] The T-Subdomain HCA algorithm includes the following three
convergence conditions, and the algorithm will converge as long as
any one condition is satisfied:
[0100] (1) When the number of iterations k (namely, the number of
finite element simulation analyses) in the outer loop exceeds a
predefined maximum number of iterations k.sub.max, the T-Subdomain
HCA algorithm ends iteration.
[0101] (2) Let p.sub.f represent the number of iterations where
infeasible solutions continuously appear, wherein an initial value
of p.sub.f is 0, and let p*.sub.f represent the maximum number of
iterations where infeasible solutions continuously appear. In the
iteration process, if the current design point is an infeasible
solution, p.sub.f=p.sub.f+1; if the current design point is a
feasible solution, p.sub.f=0. When p.sub.f>p*.sub.f, the
T-Subdomain HCA algorithm ends iteration.
[0102] (3) When the variation of design variables is very small,
namely, satisfies
i = 1 N t .OMEGA. i , j k - t .OMEGA. i , j k - 1 < 2 ,
##EQU00021##
the T-Subdomain HCA algorithm ends iteration; in the formula, N
represents the total number of cells, and .epsilon..sub.2
represents a global convergence factor.
Embodiment
[0103] Crashworthiness optimization design of a car body beam
framework is used as an example below, and the thickness of the car
body framework is optimized using T-Subdomain HCA algorithm under
the vehicle side impact loading to verify the convergence and
efficiency of the T-Subdomain HCA algorithm. The full-vehicle crash
finite element (FE) model used in this embodiment has a total
weight of 1346 kg, and includes a total of 276838 elements and
284961 nodes. The body in white is constructed mainly using shell
elements, and an engine, a gearbox, a suspension system, etc. are
established mainly using solid elements. In a full-vehicle side
impact FE model, the type of material used for deformable
structures is piecewise linear elastoplastic material, and the type
of material used by non-deformable structures is rigid material.
Contact algorithms used by the full-vehicle FE model mainly include
single surface, automatic surface-to-surface, and point-to-surface,
and a contact algorithm used for a mobile deformable barrier and a
target vehicle is automatic surface-to-surface. According to the
requirements of the regulations in "The protection of the occupants
in the event of a lateral collision" (GB 20071-2006), a mobile
deformable barrier has a weight of 950 kg and perpendicularly hits
a target vehicle at an initial velocity of 50 km/h, as shown in
FIG. 5.
[0104] In vehicle side impact loading, B-pillar, sill, front and
rear doors, and roof middle crossbeam have large deformation and
are main energy absorbing structures; A-pillar, roof rail, seat
crossbeam, and roof crossbeam are mainly used for transferring
impact load. Therefore, 34 part thicknesses of 14 assemblies such
as the A-pillar, B-pillar, sill, roof rail, front and rear doors,
rear side member, seat crossbeam, and roof crossbeam are defined as
design variables.
[0105] Defined steps of a subdomain CA model for the car body
structure are provided below:
[0106] Step (1). subdomain division: according to topological
connection characteristics of a car body structure, the design
domain is divided into several mutually independent subdomains
denoted as .OMEGA..sub.i; for example, in FIG. 6, the assemblies
such as the A-pillar, B-pillar, and sill, are respectively defined
as a subdomain .OMEGA..sub.1, a subdomain .OMEGA..sub.2, and a
subdomain .OMEGA..sub.3.
[0107] Step (2). cell definition: each component is defined as a
cell (denoted as .OMEGA..sub.i,j) in the subdomain
.OMEGA..sub.i(i=1, 2,L, l), where a subscript i of .OMEGA..sub.i,j
represents a sequence number of an ith subdomain, and a subscript j
represents the location of a current cell in the ith subdomain; in
each subdomain .OMEGA..sub.i (i=1, 2,L, l), the subscripts j of the
cells are sequentially numbered from small to large according to
principles of from inside to outside, from front to back, and from
bottom to top.
[0108] Step (3). cell state variable definition: design variables
(for example, part thicknesses) and field variables (for example,
internal energy densities) are sequentially defined for the
cells.
[0109] Step (4). cell neighborhood definition: all subdomains
.OMEGA..sub.i (i=1,2,L, l) are traversed, for cells in the same
subdomain, neighboring cells of a current cell are determined
according to magnitudes of subscripts j, and a set of the
neighboring cells of the current cell is referred to as a
neighborhood. For example, three subdomains are defined in FIG. 6,
let the cell radius equal to 1, and all cells within the cell
radius of r from the center which is the current cell are referred
to as neighboring cells of the current cell; the number {circumflex
over (N)}.sub..OMEGA..sub.1,2 of neighboring cells of the current
cell .OMEGA..sub.1,2 in the subdomain .OMEGA..sub.1 is 2, the
number {circumflex over (N)}.sub..OMEGA..sub.2,2 of neighboring
cells of the current cell .OMEGA..sub.2,1 in the subdomain
.chi..sub.2 is 1, and the number {circumflex over
(N)}.sub..OMEGA..sub.3,2 of neighboring cells of the current cell
.OMEGA..sub.3,1 in the subdomain .OMEGA..sub.3 is 1.
[0110] According to the above four steps, a total of 14 subdomains
and a total of 34 thickness variables are defined for the car
bodystructure, as shown in FIG. 6 and Table 1.
TABLE-US-00001 TABLE 1 Design variable table of car body structure
under vehicle side impact loading Subdomain Design variable
Assembly CA Initial Lower Upper name Symbol Part name Symbol Symbol
value limit limit A-pillar .OMEGA..sub.1 A-pillar inner
.OMEGA..sub.1, 1 x.sub.1 1.9 1.2 3.0 panel A-pillar .OMEGA..sub.1,
2 x.sub.2 1.9 1.0 3.0 reinforcement#1 A-pillar .OMEGA..sub.1, 3
x.sub.3 2.6 1.0 3.0 reinforcement#2 A-pillar outer .OMEGA..sub.1, 4
x.sub.4 1.4 1.2 3.0 panel B-pillar .OMEGA..sub.2 B-pillar inner
.OMEGA..sub.2, 1 x.sub.5 1.8 1.4 3.0 panel B-pillar .OMEGA..sub.2,
2 x.sub.6 2.0 1.4 3.0 reinforcement Sill .OMEGA..sub.3 Sill inner
.OMEGA..sub.3, 1 x.sub.7 1.6 1.2 3.0 panel#1 Sill inner
.OMEGA..sub.3, 2 x.sub.8 1.8 1.2 3.0 panel#2 Sill .OMEGA..sub.3, 3
x.sub.9 2.0 1.2 3.0 reinforcement Roof rail .OMEGA..sub.4 A-pillar
roof .OMEGA..sub.4, 1 x.sub.10 1.6 1.0 3.0 rail#1 A-pillar roof
.OMEGA..sub.4, 2 x.sub.11 1.6 1.0 3.0 rail#2 B-pillar roof rail
.OMEGA..sub.4, 3 x.sub.12 1.6 1.0 3.0 C-pillar roof rail
.OMEGA..sub.4, 4 x.sub.13 1.6 1.0 3.0 Front door .OMEGA..sub.5
Front door anti- .OMEGA..sub.5, 1 x.sub.14 1.9 1.0 3.0 collision
beam mounting panel#1 Front door anti- .OMEGA..sub.5, 2 x.sub.15
2.6 1.0 3.0 collision beam Front door anti- .OMEGA..sub.5, 3
x.sub.16 1.9 1.0 3.0 collision beam mounting panel#2 Front door
inner .OMEGA..sub.5, 4 x.sub.17 1.5 1.0 3.0 panel reinforcement
Rear door .OMEGA..sub.6 Rear door anti- .OMEGA..sub.6, 1 x.sub.18
1.3 1.0 3.0 collision beam mounting panel 1 Rear door anti-
.OMEGA..sub.6, 2 x.sub.19 2.0 1.0 3.0 collision beam 1 Rear door
anti- .OMEGA..sub.6, 3 x.sub.20 1.8 1.0 3.0 collision beam mounting
panel 2 Rear door inner .OMEGA..sub.6, 4 x.sub.21 2.6 1.0 3.0 panel
reinforcement Rear door anti- .OMEGA..sub.6, 5 x.sub.22 1.8 1.0 3.0
collision beam mounting panel 3 Rear door anti- .OMEGA..sub.6, 6
x.sub.23 2.6 1.0 3.0 collision beam 2 Rear door anti-
.OMEGA..sub.6, 7 x.sub.24 1.3 1.0 3.0 collision beam mounting panel
4 Rear side .OMEGA..sub.7 Rear side .OMEGA..sub.7, 1 x.sub.25 2.5
1.4 3.0 member member inner panel Rear side .OMEGA..sub.7, 2
x.sub.26 2.5 1.4 3.0 member outer panel Seat .OMEGA..sub.8 Seat
crossbeam .OMEGA..sub.8, 1 x.sub.27 2.0 1.0 3.0 crossbeam lining
panel Seat crossbeam .OMEGA..sub.8, 2 x.sub.28 1.5 1.2 3.0 Front
side .OMEGA..sub.9 Front side .OMEGA..sub.9, 1 x.sub.29 1.2 1.0 3.0
member rear member rear section section Seat rear .sup.
.OMEGA..sub.10 Seat rear .sup. .OMEGA..sub.10, 1 x.sub.30 2.0 1.2
3.0 crossbeam crossbeam Rear floor .sup. .OMEGA..sub.11 Rear floor
front .sup. .OMEGA..sub.11, 1 x.sub.31 1.4 1.2 3.0 front crossbeam
crossbeam Roof front .sup. .OMEGA..sub.12 Roof front .sup.
.OMEGA..sub.12, 1 x.sub.32 1.4 1.0 3.0 crossbeam crossbeam Roof
middle .sup. .OMEGA..sub.13 Roof middle .sup. .OMEGA..sub.13, 1
x.sub.33 2.0 1.0 3.0 crossbeam crossbeam Roof rear .sup.
.OMEGA..sub.14 Roof rear .sup. .OMEGA..sub.14, 1 x.sub.34 1.4 1.0
3.0 crossbeam crossbeam
[0111] Maximum intrusion amount and maximum intrusion velocity at
B-pillar waistline location and maximum intrusion amount and
maximum intrusion velocity at B-pillar pelvis location are
respectively selected as crashworthiness indexes and output
responses of the full-vehicle side crash, which are respectively
denoted as d.sub.1(x), v.sub.1(x), d.sub.2(x), and v.sub.2(x).
[0112] In this embodiment, minimization of the total weight of the
34 parts in Table 1 is used as an objective function, and the
maximum intrusion amount and the maximum intrusion velocity at the
B-pillar waistline location and pelvis location are used as
constraint functions. The initial total weight of the 34 parts is
108.30 kg, initial maximum intrusion amounts are respectively
252.80 mm and 234.40 mm, and initial maximum intrusion velocities
are respectively 9.00 m/s and 8.30 m/s. It is obvious that the
initial full-vehicle crash model cannot meet the requirements of
the regulations in "The protection of the occupants in the event of
a lateral collision" (GB 20071-2006). In order to meet the
requirements of the regulations, the maximum intrusion amount and
the maximum intrusion velocity should be less than or equal to 180
mm and 8 m/s respectively, and corresponding optimization equations
are:
{ min M ( x ) s . t . d 1 ( x ) .ltoreq. 180 d 2 ( x ) .ltoreq. 180
v 1 ( x ) .ltoreq. 8 v 2 ( x ) .ltoreq. 8 x L .ltoreq. x .ltoreq. x
U , x = ( x 1 , x 2 , , x 33 , x 34 ) T ( 20 ) ##EQU00022##
[0113] where x.sup.L is lower boundary of design variable, and
x.sup.U is upper boundary of design variable.
[0114] Usually, a horizontal target internal energy density
function (horizontal IED target, HIED*) (shown in formula (21)) is
calculated in each iteration of an inner loop of a conventional HCA
method, and then a cell thickness is updated according to a certain
control strategy, so that a current mass of the inner loop
converges to a target mass.
S * ( h + 1 , k ) = S * ( h , k ) M ( h , k ) M * ( k ) ( 21 )
##EQU00023##
[0115] in the formula, M*.sup.(k) represents a target mass obtained
by updating in the kth outer loop, M.sup.(h,k) represents a current
mass obtained in the kth outer loop and the hth inner loop,
S*.sup.(h,k) is a horizontal target internal energy density in the
kth outer loop and the hth inner loop, and S*.sup.(h+1,k)
represents a horizontal target internal energy density in the kth
outer loop and the (h+1)th inner loop.
[0116] In this embodiment, a T-Subdomain HCA algorithm in which a
horizontal target internal energy density function used in inner
loop is referred to as "T-Subdomain HCA #1" algorithm, and the
T-Subdomain HCA algorithm in which a step target internal energy
density function used in inner loop is referred to as "T-Subdomain
HCA #2" algorithm. In order to verify the convergence and
efficiency of the T-Subdomain HCA #2 algorithm in the present
invention, the T-Subdomain HCA #1 and T-Subdomain HCA #2 algorithms
and a parallel EGO algorithm based on a pseudo CEI criterion
(Parallel Efficient Global Optimization based on pseudo constrained
expected improvement, "parallel EGO-PCEI" for short) are separately
used for solving the optimization equation (20), and optimization
results and the numbers of finite element analyses of the
aforementioned three methods are compared. For the parameter
setting of the T-Subdomain HCA #1 and T-Subdomain HCA #2
algorithms, see Table 2 for details. For the parameter setting of
the parallel EGO-PCEI algorithm, see Table 3 for details.
TABLE-US-00002 TABLE 2 Parameter setting of T-Subdomain HCA
algorithm T-Subdomain T-Subdomain Parameter name Symbol HCA#1 HCA#2
Cell number N 34 34 Subdomain number l 14 14 Cell radius r 1 1
Width threshold of "step interval" H.sub.threshold -- 4 Target
internal energy V.sub.threshold -- 1.1 density threshold
coefficient in "step interval" Proportional control coefficient
K.sub.p 0.03 0.03 of cell thickness variation Integral control
coefficient of cell K.sub.i 0.0001 0.0001 thickness variation
Differential control coefficient K.sub.d 0.0001 0.0001 of cell
thickness variation Proportionality coefficient of K.sub.q 0.1 0.1
target mass penalty Maximum penalty of target mass .DELTA.M 4 kg 4
kg Maximum number of P*.sub.f 8 8 iterations where infeasible
solutions continuously appear Maximum number of k.sub.lmax 2000
2000 iterations in inner loop Maximum number of k.sub.max 50 50
iterations in outer loop Convergence coefficient .epsilon..sub.1
0.001 0.001 of inner loop Global convergence coefficient
.epsilon..sub.2 0.001 0.001
TABLE-US-00003 TABLE 3 Parameter setting of parallel EGO-PCEI
algorithm Parameter Parameter name Symbol value Number of design
variables N.sub.v 34 Number of initial samples N.sub.initial 4
Number of parallel calculations N.sub.parallel 4 Maximum number of
finite element analyses Max.sub.FEA 300
[0117] FIGS. 7A-7C illustrate curves of iteration processes of a
T-Subdomain HCA #1 algorithm. According to FIGS. 7A-7C, the
T-Subdomain HCA #1 algorithm converges after 48 iterations, an
optimal solution is found in the 3.sup.2nd iteration, and a total
of 48 finite element analyses are conducted. FIGS. 8A-8C illustrate
curves of iteration processes of a T-Subdomain HCA #2 algorithm.
According to FIGS. 8A-8C, the T-Subdomain HCA #2 algorithm
converges after 49 iterations, an optimal solution is found in the
28.sup.th iteration, and a total of 49 finite element analyses are
conducted. Upon comparison between FIGS. 7A-7C and FIGS. 8A-8C, a
target function of the T-Subdomain HCA #1 algorithm no longer
decreases in the vicinity of 100 kg and rapidly converges to a
local optimal solution, while a target function of the T-Subdomain
HCA #2 algorithm still rapidly decreases after reaching 90 kg and
the algorithm converges when decreasing to 85.40 kg. FIG. 9A-9C
illustrate curves of iteration processes of a parallel EGO-PCEI
algorithm. According to FIGS. 9A-9C, a target function of the
parallel EGO-PCEI algorithm converges more slowly after decreasing
to 90 kg, a global optimal solution is found in the 68.sup.th
iteration, and the algorithm reaches a convergence condition after
300 finite element analyses are conducted. Table 4 records
statistics of the number of finite element analyses when the
T-Subdomain HCA #1 algorithm, the T-Subdomain HCA #2 algorithm, and
the parallel EGO-PCEI algorithm converge to the optimal solutions
and response values of the optimal solutions.
TABLE-US-00004 TABLE 4 Comparison between optimal solutions of
T-Subdomain HCA#1, T-Subdomain HCA#2, and parallel EGO-PCEI
algorithms parallel T-Subdomain T-Subdomain EGO- HCA#1 HCA#2 PCEI
M(x) (kg) 99.36 85.40 86.45 d.sub.1( x) (mm) 154.40 134.60 162.70
d.sub.2(x) (mm) 171.10 176,70 180.00 v.sub.1(x) (m/s) 7.19 5.97
6.65 v.sub.2(x) (m/s) 7.02 6.60 6.89 Number of finite 37 28 273
element analyses when converging to optimal solution Total number
of finite 48 49 300 element analyses
[0118] Upon comparison and analysis of FIGS. 7A-7C, FIG. 8A-8C,
FIG. 9A-9C, and Table 5, the T-Subdomain HCA #1 algorithm easily
traps into a local optimal solution; the T-Subdomain HCA #2
algorithm not only has a high optimization efficiency, but also has
a stronger global search capability; the global optimization
capability of the T-Subdomain HCA #2 algorithm equals that of the
parallel EGO-PCEI algorithm, but the optimization efficiency
thereof is obviously higher than that of the parallel EGO-PCEI
algorithm. Thus, the T-Subdomain HCA algorithm provided in the
present invention has high optimization efficiency and precision
for solving time-consuming and multi-variable nonlinear dynamic
response optimization problems, and meanwhile the effectiveness of
the algorithm is verified.
[0119] Next, the specific effects of using a T-Subdomain HCA
algorithm based on a target internal energy density function to
perform crashworthiness optimization and lightweight design for a
car body structure under vehicle side impact loading. Table 5 lists
the total weight of the 34 parts and performance improvement
percentage of vehicle side impact before and after optimization.
According to Table 5, the optimal solution obtained in the
T-Subdomain HCA algorithm based on the step target internal energy
density function can achieve a weight reduction effect of 21.64%,
and meanwhile, d.sub.1(x) drops by 46.76%, d.sub.2(x) drops by
24.62%, v.sub.1(x) drops by 34.22%, and v.sub.2(X) drops by 20.48%.
This algorithm not only reduces the total weight of the 34 parts to
a large extent, but also significantly improves the safety in case
of vehicle side impact.
TABLE-US-00005 TABLE 5 Performance improvement percentages before
and after optimization M(x) d.sub.1(x) d.sub.2(x) v.sub.1(x)
v.sub.2(x) (kg) (mm) (mm) (m/s) (m/s) Initial 108.30 252.80 234.40
9.00 8.30 design Optimal 85.40 134.60 176.70 5.92 6.60 solution
Relative -21.64% -46.76% -24.62% -34.22% -20.48% change rate
(%)
[0120] FIGS. 10A-10B and 11A-11B compare curves of intrusion
amounts and intrusion velocities at B-pillar waistline location and
pelvis location before and after optimization. FIGS. 12A-12B
compare car body deformation patterns before and after
optimization. According to FIGS. 10A-10B and FIGS. 12A-12B, the
intrusion amount and intrusion velocity of the optimal solution are
improved to a large extent as compared with the initial design; the
B-pillar and roof middle crossbeam of the optimal solution are
reinforced, and deformation patterns thereof are obviously improved
as compared with the initial design.
[0121] The described embodiment is a preferred embodiment of the
present invention, but the present invention is not limited to the
aforementioned embodiment. Any obvious improvements, substitutions
or modifications that can be made by those skilled in the art
without departing from the essential content of the present
invention shall fall within the protection scope of the present
invention.
* * * * *